On the Numerical Evaluation of Wall Shear Stress Using the Finite Element Method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10502720" target="_blank" >RIV/00216208:11320/25:10502720 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.mLRisHtOY" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=.mLRisHtOY</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/cnm.70086" target="_blank" >10.1002/cnm.70086</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Numerical Evaluation of Wall Shear Stress Using the Finite Element Method

Popis výsledku v původním jazyce

Wall shear stress (WSS) is a crucial hemodynamic quantity extensively studied in cardiovascular research, yet its numerical computation is not straightforward. This work compares WSS results obtained from two different finite element discretizations, quantifies the differences between continuous and discontinuous stresses, and introduces a modified variationally consistent method for WSS evaluation through the formulation of a boundary-flux problem. Two benchmark problems are considered: a 2D Stokes flow on a unit square and a 3D Poiseuille flow through a cylindrical pipe. These are followed by investigations of steady-state Navier-Stokes flow in two image-based, patient-specific aneurysms. The study focuses on P1/P1 stabilized and Taylor-Hood P2/P1 mixed finite elements for velocity and pressure. WSS is computed using either the proposed boundary-flux method or as a projection of tangential traction onto first order Lagrange (P1), discontinuous Galerkin first order (DG-1), or discontinuous Galerkin zero order (DG-0) space. For the P1/P1 stabilized element, the boundary-flux and P1 projection methods yielded equivalent results. With the P2/P1 element, the boundary-flux evaluation demonstrated faster convergence in the Poiseuille flow example but showed increased sensitivity to pressure field inaccuracies in image-based geometries compared to the projection method. Furthermore, a paradoxical degradation in WSS accuracy was observed when combining the P2/P1 element with fine boundary-layer meshes on a cylindrical geometry, an effect attributed to inherent geometric approximation errors. In aneurysm geometries, the P2/P1 element exhibited superior robustness to mesh size when evaluating average WSS and low shear area (LSA), outperforming the P1/P1 stabilized element. Projecting discontinuous finite element functions into continuous spaces can introduce artifacts, such as the Gibbs phenomenon. Consequently, it is crucial to carefully select the finite element space for boundary stress calculations, not only in applications involving WSS computations for aneurysms.

Název v anglickém jazyce

On the Numerical Evaluation of Wall Shear Stress Using the Finite Element Method

Popis výsledku anglicky

Wall shear stress (WSS) is a crucial hemodynamic quantity extensively studied in cardiovascular research, yet its numerical computation is not straightforward. This work compares WSS results obtained from two different finite element discretizations, quantifies the differences between continuous and discontinuous stresses, and introduces a modified variationally consistent method for WSS evaluation through the formulation of a boundary-flux problem. Two benchmark problems are considered: a 2D Stokes flow on a unit square and a 3D Poiseuille flow through a cylindrical pipe. These are followed by investigations of steady-state Navier-Stokes flow in two image-based, patient-specific aneurysms. The study focuses on P1/P1 stabilized and Taylor-Hood P2/P1 mixed finite elements for velocity and pressure. WSS is computed using either the proposed boundary-flux method or as a projection of tangential traction onto first order Lagrange (P1), discontinuous Galerkin first order (DG-1), or discontinuous Galerkin zero order (DG-0) space. For the P1/P1 stabilized element, the boundary-flux and P1 projection methods yielded equivalent results. With the P2/P1 element, the boundary-flux evaluation demonstrated faster convergence in the Poiseuille flow example but showed increased sensitivity to pressure field inaccuracies in image-based geometries compared to the projection method. Furthermore, a paradoxical degradation in WSS accuracy was observed when combining the P2/P1 element with fine boundary-layer meshes on a cylindrical geometry, an effect attributed to inherent geometric approximation errors. In aneurysm geometries, the P2/P1 element exhibited superior robustness to mesh size when evaluating average WSS and low shear area (LSA), outperforming the P1/P1 stabilized element. Projecting discontinuous finite element functions into continuous spaces can introduce artifacts, such as the Gibbs phenomenon. Consequently, it is crucial to carefully select the finite element space for boundary stress calculations, not only in applications involving WSS computations for aneurysms.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/NU22-08-00124" target="_blank" >NU22-08-00124: Modelování toku v intrakraniálních cévách ve vztahu ke změnám endotelu a rozvoji intrakraniálních aneuryzmat</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal for Numerical Methods in Biomedical Engineering

ISSN

2040-7939

e-ISSN

2040-7947

Svazek periodika

41

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

19

Strana od-do

e70086

Kód UT WoS článku

001583201900007

EID výsledku v databázi Scopus

2-s2.0-105015580444